Apparatus and processes for photosynthetic activity measurement and mapping

ABSTRACT

A method for determining chlorophyll content of a plant comprises capturing a first image comprising light transmitted through a leaf of a plant; capturing a second image comprising light reflected from the leaf of the plant; estimating, from a plurality of pixels in the first image, a transmissive chlorophyll concentration value of the leaf; estimating a reflectance chlorophyll concentration value for the leaf from a plurality of pixels in the second image using bidirectional reflectance parameters for which a variance of the reflectance chlorophyll concentration value across the plurality of pixels in the second image is reduced; and determining an estimated chlorophyll concentration value for the plant based at least on the transmissive chlorophyll concentration value and the reflectance chlorophyll concentration value.

RELATED APPLICATIONS

This application claims priority under 35 U.S.C. §119(e) to U.S.Provisional App. No. 62/160,881, entitled “APPARATUS AND PROCESSES FOR APHOTOSYNTHETIC ACTIVITY MAPPING APPLICATION,” filed May 13, 2015, whichapplication is incorporated herein by reference in its entirety.

BACKGROUND

Nitrogen fertilizer is one of the main costs associated with growingfood crops, including grain crops such as corn, wheat, and rice. To apoint, nitrogen increases crop yield at a very cost-efficient rate;beyond that point, some amount of over-application does not harm theplant. Farmers therefore often err on the side of caution byover-applying nitrogen fertilizer to their crops. World-wide annualconsumption of nitrogen fertilizer is 500 million short tons, up to anestimated 50% of which is not needed to achieve optimum yield.

There are downsides to the over-application of nitrogen fertilizer,including the needless expense to the grower and the risks posed towater and other aspects of the ecosystem affected by runoff. It wouldtherefore be advantageous to accurately identify an optimal amount ofnitrogen fertilizer to be applied to maximize yield of the crop withoutusing more than needed.

Nitrogen content and chlorophyll content in a plant are interrelated, soby estimating the amount of chlorophyll in a plant, the amount ofnitrogen present (and therefore the amount of nitrogen to be applied)can be determined. Known techniques for estimating chlorophyll fromimages of the plant rely on the color of the leaf. Yet “color” describesthe response of the eyes and brain to the visible spectrum, and istherefore inapplicable and unreliable in computer-based chlorophyllmeasurement. Estimating chlorophyll content also requires informationabout the structure of the leaf, including its index of refraction,which varies from species to species. Known methods typically used a“published” value of a leaf model parameter, N. Yet this approximationof N for a given leaf does not take into account the actual variationsin N from leaf to leaf.

SUMMARY OF THE INVENTION

Aspects and embodiments are directed to apparatus and methods forprocessing digital images of plant leaves to estimate a level ofchlorophyll in the plant. Images of light transmitted through, andreflected from, the leaf is used. The issue of bidirectional reflectanceis addressed by assigning initial bidirectional reference parameters tothe pixels of the image of reflected light and estimating a chlorophylllevel for each pixel using those parameters. The bidirectional referenceparameters are iterated according to the estimated chlorophyll level,and the process repeats until a chlorophyll level of the leaf isconverged upon for which there is minimal variance across the pixels.The difference between the chlorophyll estimates obtained using thetransmitted and reflected light is used to re-estimate a model parameterrelating to an index of refraction of the leaf, and new estimates aregenerated using the revised model parameter.

One or more spot chlorophyll measurements taken in such a manner can beused to correct and calibrate overhead imagery of the crop, allowing forthe creation of an overhead chlorophyll model refined by the spotmeasurements. The chlorophyll model is used to generate a nitrogensufficiency map, which in turn allows for the creation ofrecommendations for the application of nitrogen at locations in thefield where the nitrogen level is insufficient. Spot yield measurementsand historical data can be used to further refine the overhead model andnitrogen recommendations.

According to one aspect, a method for determining chlorophyll content ofa plant includes capturing a first image comprising light transmittedthrough a leaf of a plant; capturing a second image comprising lightreflected from the leaf of the plant; estimating, from a plurality ofpixels in the first image, a transmissive chlorophyll concentrationvalue of the leaf; estimating a reflectance chlorophyll concentrationvalue for the leaf from a plurality of pixels in the second image usingbidirectional reflectance parameters for which a variance of thereflectance chlorophyll concentration value across the plurality ofpixels in the second image is reduced; and determining an estimatedchlorophyll concentration value for the plant based at least on thetransmissive chlorophyll concentration value and the reflectancechlorophyll concentration value.

According to one embodiment, the transmissive chlorophyll concentrationvalue and the reflectance chlorophyll concentration value are determinedusing a leaf model parameter, and the method further includesestimating, from the transmissive chlorophyll concentration value andthe reflectance chlorophyll concentration value, a revised leaf modelparameter; and determining a second transmissive chlorophyllconcentration value and a second reflectance chlorophyll concentrationvalue using the revised leaf model parameter. According to a furtherembodiment, the revised leaf model parameter is estimated based on adifference between the transmissive chlorophyll concentration value andthe reflectance chlorophyll concentration value. According to yetanother embodiment, estimating, from the plurality of pixels in thefirst image, the transmissive chlorophyll concentration value of theleaf includes determining, from sensor spectral response characteristicsof each pixel in the plurality of pixels in the first image, atriangular greenness index (TGI) for the pixel.

According to one embodiment, the method further includes capturing athird image comprising light passed through a first medium and a fourthimage comprising light passed through a second medium, the first mediumand second medium having transmissive characteristics corresponding toknown transmissive chlorophyll levels; and adjusting the transmissivechlorophyll concentration value of the leaf with reference to the knowntransmissive chlorophyll levels. According to a further embodiment, thefirst medium has transmissive characteristics corresponding to a knownlow transmissive chlorophyll level, and the second medium hastransmissive characteristics corresponding to a known high transmissivechlorophyll level.

According to another embodiment, the method further includes estimating,using a bidirectional reflectance parameter for each pixel in theplurality of pixels, a first reflectance chlorophyll concentration pixelvalue for each pixel in the plurality of pixels; determining a firstvariance of the first reflectance chlorophyll concentration pixel valueacross the plurality of pixels; modifying the bidirectional reflectanceparameter for at least one pixel in the plurality of pixels; estimating,using the modified bidirectional reflectance parameter for the at leastone pixel, a second reflectance chlorophyll concentration pixel valuefor each pixel in the plurality of pixels; determining a second varianceof the second reflectance chlorophyll concentration pixel value acrossthe plurality of pixels; responsive to the first variance being lessthan the second variance, estimating the reflectance chlorophyllconcentration value based on the first reflectance chlorophyllconcentration pixel value of the leaf for each pixel in the plurality ofpixels; and responsive to the second variance being less than the firstvariance, estimating the reflectance chlorophyll concentration valuebased on the second reflectance chlorophyll concentration pixel value ofthe leaf for each pixel in the plurality of pixels.

According to a further embodiment, modifying the bidirectionalreflectance parameter for at least one pixel in the plurality of pixelsincludes, responsive to the at least one pixel in the plurality ofpixels having a relatively high first reflectance chlorophyllconcentration pixel value, adjusting the bidirectional reflectanceparameter of the at least one pixel to be lower; and responsive to theat least one pixel in the plurality of pixels having a relatively lowfirst reflectance chlorophyll concentration pixel value, adjusting thebidirectional reflectance parameter of the at least one pixel to behigher. According to a further embodiment, estimating the reflectancechlorophyll concentration value based on the second reflectancechlorophyll concentration pixel value of the leaf for each pixel in theplurality of pixels includes determining a mean of the secondreflectance chlorophyll concentration pixel value of the leaf for theplurality of pixels.

According to a further embodiment, the method further includesexcluding, from the determination of the mean, pixels having a modifiedbidirectional reflectance parameter not within a defined deviationamount.

According to a still further embodiment, the bidirectional reflectanceparameter is an initial bidirectional reflectance parameter, and themethod further includes setting an initial bidirectional reflectanceparameter for at least one pixel in the plurality of pixels, the initialbidirectional reflectance parameter determined by the sensor spectralresponse measurement of the at least one pixel.

According to a still further embodiment, the method further includessetting a first initial bidirectional reflectance parameter of 0.6 forat least one pixel having a highest sensor spectral response measurementin the plurality of pixels, and setting a second initial bidirectionalreflectance parameter of 0.0 for at least one pixel having a lowestsensor spectral response measurement in the plurality of pixels.

According to one embodiment, the plant is a first plant, and the methodfurther includes estimating a second transmissive chlorophyllconcentration value and a second reflectance chlorophyll concentrationvalue for at least a second plant in a crop field including the firstplant; and generating a model of plant health for the crop field basedat least on the transmissive chlorophyll concentration value, thereflectance chlorophyll concentration value, the second transmissivechlorophyll concentration value and the second reflectance chlorophyllconcentration value. According to a further embodiment, the model ofplant health for the crop field is a chlorophyll model indicating anestimated chlorophyll level of plants in a plurality of locations in thecrop field.

According to another embodiment, the plant is a corn plant.

According to another aspect, an image processing system includes amemory; an image receiving component; and a processor configured tocapture a first image comprising light transmitted through a leaf of aplant; capture a second image comprising light reflected from the leafof the plant; estimate, from a plurality of pixels in the first image, atransmissive chlorophyll concentration value of the leaf; estimate areflectance chlorophyll concentration value for the leaf from aplurality of pixels in the second image using bidirectional reflectanceparameters for which a variance of the reflectance chlorophyllconcentration value across the plurality of pixels in the second imageis reduced; and determine an estimated chlorophyll concentration valuefor the plant based at least on the transmissive chlorophyllconcentration value and the reflectance chlorophyll concentration value.

According to one embodiment, the image receiving component is a digitalcamera of a mobile device. According to another embodiment, the imageprocessing system further includes an optical reference having a firstmedium and a second medium, the first medium and second medium havingtransmissive characteristics corresponding to known transmissivechlorophyll levels, and the processor is further configured to capture athird image comprising light passed through the first medium and afourth image comprising light passed through the second medium; andadjust the transmissive chlorophyll concentration value of the leaf withreference to the known transmissive chlorophyll levels.

According to another embodiment, the processor is further configured toestimate, using a bidirectional reflectance parameter for each pixel inthe plurality of pixels, a first reflectance chlorophyll concentrationpixel value for each pixel in the plurality of pixels; determine a firstvariance of the first reflectance chlorophyll concentration pixel valueacross the plurality of pixels; modify the bidirectional reflectanceparameter for at least one pixel in the plurality of pixels; estimate,using the modified bidirectional reflectance parameter for the at leastone pixel, a second reflectance chlorophyll concentration pixel valuefor each pixel in the plurality of pixels; determine a second varianceof the second reflectance chlorophyll concentration pixel value acrossthe plurality of pixels; responsive to the first variance being lessthan the second variance, estimate the reflectance chlorophyllconcentration value based on the first reflectance chlorophyllconcentration pixel value of the leaf for each pixel in the plurality ofpixels; and responsive to the second variance being less than the firstvariance, estimate the reflectance chlorophyll concentration value basedon the second reflectance chlorophyll concentration pixel value of theleaf for each pixel in the plurality of pixels.

According to a further embodiment, the processor is further configuredto modify the bidirectional reflectance parameter for at least one pixelin the plurality of pixels by, responsive to the at least one pixel inthe plurality of pixels having a relatively high first reflectancechlorophyll concentration pixel value, adjusting the bidirectionalreflectance parameter of the at least one pixel to be lower; andresponsive to the at least one pixel in the plurality of pixels having arelatively low first reflectance chlorophyll concentration pixel value,adjusting the bidirectional reflectance parameter of the at least onepixel to be higher.

According to another aspect, a method of determining a nitrogen contentof a field crop includes determining, from an image of an individualplant leaf from a first plant in a field, an estimate of a chlorophyllconcentration value of the first plant in a first region in the field;detecting, in an overhead image of the field, an overhead sensorspectral response measurement of at least one second plant in the firstregion in the field; and generating, based on the estimate of thechlorophyll concentration value of the individual plant leaf and theoverhead sensor spectral response measurement of the at least one secondplant, a map of estimated chlorophyll concentrations of plants in aportion of the field.

According to a further embodiment, the overhead sensor spectral responsemeasurement of the at least one second plant is a triangular green index(TGI). According to a further embodiment, the method further includesdetermining, from a ground-based image of at least one third plant andsurrounding soil in the first region, a ground-based sensor spectralresponse measurement of the at least one third plant; and adjusting theoverhead sensor spectral response measurement of the at least one secondplant based on the ground-based sensor spectral response measurement.

According to a further embodiment, the method includes identifying atleast one dimension of a row of plants in which the at least one thirdplant is located. According to a further embodiment, the method includesgenerating, based on the map of estimated chlorophyll concentrations ofplants in a portion of the field, at least one recommendation forapplying nitrogen to the first region of the field.

According to a further embodiment, the method includes determining, froman image of a grain seed head of a third plant in the first region ofthe field, an estimated yield of the third plant; and modifying the atleast one recommendation for applying nitrogen to the first region ofthe field based on the estimated yield of the third plant.

Still other aspects, embodiments, and advantages of these exemplaryaspects and embodiments are discussed in detail below. Embodimentsdisclosed herein may be combined with other embodiments in any mannerconsistent with at least one of the principles disclosed herein, andreferences to “an embodiment,” “some embodiments,” “an alternateembodiment,” “various embodiments,” “one embodiment” or the like are notnecessarily mutually exclusive and are intended to indicate that aparticular feature, structure, or characteristic described may beincluded in at least one embodiment. The appearances of such termsherein are not necessarily all referring to the same embodiment.

BRIEF DESCRIPTION OF THE DRAWINGS

Various aspects of at least one embodiment are discussed below withreference to the accompanying figures, which are not intended to bedrawn to scale. The figures are included to provide illustration and afurther understanding of the various aspects and embodiments, and areincorporated in and constitute a part of this specification, but are notintended as a definition of the limits of the invention. In the figures,each identical or nearly identical component that is illustrated invarious figures is represented by a like numeral. For purposes ofclarity, not every component may be labeled in every figure. In thefigures:

FIG. 1 illustrates an exemplary method of estimating the chlorophylllevel of a leaf as discussed in various embodiments herein;

FIG. 2A illustrates an exemplary first image (reproduced in grayscale)of light transmitted through a leaf according to aspects of theinvention;

FIG. 2B illustrates an exemplary second image (reproduced in grayscale)of light reflected from a leaf according to aspects of the invention;

FIG. 3 illustrates an optical reference card for calibrating chlorophyllmeasurements according to aspects of the invention;

FIG. 4 illustrates an exemplary method of estimating a chlorophyll levelfrom the leaf of the second image of FIG. 2B as discussed in variousembodiments herein;

FIG. 5 illustrates an exemplary overhead model of chlorophyll in a fieldaccording to aspects of the invention;

FIG. 6 illustrates an exemplary method of using spot chlorophyllmeasurements to generate a chlorophyll map of a field as discussed invarious embodiments herein; and

FIG. 7 is a block diagram of one example of a computer system on whichaspects and embodiments of the present invention may be implemented.

DETAILED DESCRIPTION

The ability to capture and process images of leaves and other foliage,and used those images to estimate a chlorophyll level of the plant,enables a user to estimate an amount of nitrogen available to the plant,and, if necessary, an amount of nitrogen to be applied via “side dress”fertilizing or other means. Aspects and embodiments are directed tocapturing a first image of light transmitted through a leaf, andcapturing a second image of light reflected off the leaf. The firstimage is processed to estimate a chlorophyll a+b level from thetransmitted light using coefficients related to N, the parameter thatmodels the leaf's index of refraction.

The second image is processed to estimate a chlorophyll a+b level fromthe reflected light using coefficients related to N. To reduce theeffect of glint/glare, incidence angle, and other complicating factorsintroduced in when reflected light is photographed, each pixel of theimage is assigned an initial bidirectional reflectance parameter(Bspec). A chlorophyll a+b level is estimated from the reflected lightusing the initial Bspec value for each pixel. The initial Bspec valuesare then adjusted based on the estimated chlorophyll level for eachpixel, on the assumption that the chlorophyll level will be relativelyconsistent throughout the leaf. The adjustment of Bspec values continuesin an iterative manner until a combination of Bspec values is found forthe pixels that yields minimal variance of estimated chlorophyll acrossthe pixels. By converging on the estimated chlorophyll level in thismanner, the effect of Bpsec sensitivity in determining estimatedchlorophyll is reduced.

Once estimates of the chlorophyll levels have been determined from thetransmitted light and the reflected light, the two measurements can becompared, and their relationship can be used to re-estimate the modelparameter N. The chlorophyll levels can then be re-estimated using therevised value of N, allowing for a more accurate chlorophyll estimate.

A number of spot measurements of chlorophyll taken in this manner can beused to generate a full chlorophyll model of the field, which in turncan be used to generate nitrogen sufficiency maps.

It is to be appreciated that embodiments of the methods and apparatusesdiscussed herein are not limited in application to the details ofconstruction and the arrangement of components set forth in thefollowing description or illustrated in the accompanying drawings. Themethods and apparatuses are capable of implementation in otherembodiments and of being practiced or of being carried out in variousways. Examples of specific implementations are provided herein forillustrative purposes only and are not intended to be limiting. Also,the phraseology and terminology used herein is for the purpose ofdescription and should not be regarded as limiting. The use herein of“including,” “comprising,” “having,” “containing,” “involving,” andvariations thereof is meant to encompass the items listed thereafter andequivalents thereof as well as additional items. References to “or” maybe construed as inclusive so that any terms described using “or” mayindicate any of a single, more than one, and all of the described terms.Any references to front and back, left and right, top and bottom, upperand lower, and vertical and horizontal are intended for convenience ofdescription, not to limit the present systems and methods or theircomponents to any one positional or spatial orientation.

FIG. 1 is a flow diagram for one example of a method 100 for determiningchlorophyll content of a plant.

Method 100 begins at step 110.

At step 120, a first image is captured comprising light transmittedthrough a leaf of a plant grown in a crop field, and at step 130, asecond image is captured comprising light reflected from the leaf of theplant. The first image and the second image may be captured by a digitalcamera, or by a mobile device (e.g., a cell phone or tablet) with acamera and image-capturing capabilities. The use of a mobile device mayallow the images to be captured in a field of crops (e.g., a corn field)in which the plant is growing. In other embodiments, the image is notdirectly captured, but may be received over a network, on a disk, orotherwise provided to the system for processing.

To capture the first image of light transmitted through the leaf of theplant grown in the crop field, the leaf is held directly adjacent to andin contact with the lens of the camera. In some embodiments, the plantis a corn plant, and the leaf is a husk of the corn. It will beappreciated, however, that the embodiments disclosed herein can becarried out on leaves of a variety of plants without departing from thespirit of the disclosure. A clamp, fixture, or other component may beutilized to hold the leaf at a distance and orientation relative to thelens suitable for creating the first image. With the leaf in position,the first image is created when light passes through the leaf andstrikes the camera sensor on which the image is formed.

Exemplary first image 200A and second image 200B are seen in FIGS. 2Aand 2B, respectively. Though the first image 200A and the second image200B are shown here in grayscale for ease of reproduction, it is to beexpected that the first image 200A and the second image 200B willinclude one or more shades of green color depending on the type of leafand/or its chlorophyll content.

To capture the second image of light reflected from the leaf of theplant, the leaf may be held at a set distance from the camera lens. Aclamp, fixture, or other component may be utilized to hold the leaf at adistance and orientation relative to the lens suitable for creating thesecond image. With the leaf in position, the second image is createdwhen light reflects off the leaf and strikes the camera sensor on whichthe image is formed.

An exemplary second image 200B is seen in FIG. 2B. Because the secondimage 200B is created by reflected light, areas of different brightnessare present due to the orientation and characteristics of the leaf, thelight source (e.g., the sun), and/or the camera lens used to capture thesecond image. For example, a “glint” of light reflected from the leafcan be seen in an area of relatively high brightness surrounding pixel210. A relatively darker area of the leaf, due to the relatively loweramount of light it reflects, can be seen in an area of relatively lowbrightness surrounding pixel 220.

The first image and the second image may be created using the same leaf,or may be created using different leaves having certain characteristicsin common, including color, thickness, location of the plant from whichit was harvested, elapsed time since picking, or other characteristics.

Images created by light that is either transmitted through the leaf (asin the first image) or reflected off the leaf (as in the second image)are sensitive to differences in lighting conditions, and images capturedin certain lighting conditions may allow the embodiments describedherein to be performed with a higher degree of accuracy. In someembodiments, therefore, certain lighting conditions may be enforced orsuggested. For example, it may be a requirement that the first imageand/or second image are captured during periods of bright sunlight. Itmay also be a requirement that the second image (of reflected light) becaptured when the sun is substantially overhead, or in another knownposition. Information about weather forecasts, sun position, and othermeteorological information may be accessed to aid in predicting orotherwise determining suitable conditions for capturing the first imageand/or the second image. In some embodiments, suggestions orinstructions for suitable times and/or weather conditions may beprovided. For example, the mobile device may display informationindicating that suitable conditions are expected between 11:15 am and1:45 pm on an upcoming day during which to capture the second image. Insome embodiments, artificial light sources may be used. Differentlighting conditions may be suitable for different devices according totheir digital camera sensitivity functions. In some embodiments,sensitivity functions for known device models may be accessed from adatabase in determining whether lighting conditions are suitable. Inother embodiments, the sensitivity function of the device may beestimated or determined using known techniques as part of a pre-processor calibration process.

Additional constraints may be imposed under which the first image and/orthe second image will be captured. For example, attempts to capture thesecond image may be affected by bright areas of light, or glint,reflecting off the surface of the leaf. In some embodiments, the mobiledevice may provide an indication that undesirable lighting conditions(like excessive glint) are present, and may delay attempts to capturethe second image until the lighting conditions are corrected.

Once captured, the size or other characteristics of the first imageand/or second image may also be validated or modified as necessary. Forexample, if the image is of too low a resolution, size, contrast, orsharpness, it may be assumed that the method cannot be performed on theimage in a manner yielding sufficiently accurate results. As a result,an attempt to perform the method on an image having an inadequateresolution (e.g., less than 2 megapixels), size, contrast, or sharpnessmay be aborted by the system, and an error message may be displayed onthe mobile device or elsewhere indicating that the image is deficient,as well as information identifying the deficiency.

On the other hand, while digital cameras and devices are currently ableto capture relatively high-resolution images, and typically do so bydefault, it may be determined in some embodiments that such highresolution is not necessary for performance of the method. Furthermore,the large file sizes associated with such high-resolution images mayrequire an unnecessary amount of time and resources to process. Theimage may therefore be downsampled to a lower resolution that reducesfile size while still providing sufficient resolution for the imageprocessing steps described herein. Downsampling the image to astandardized resolution may also simplify subsequent processing steps,as there would be no need to provide for the processing of images havingdifferent resolutions. In a preferred embodiment, the image may bedownsampled to 2 megapixels. In other embodiments, the resultingresolution may be set by the system or a user, or may be determined atruntime by taking into account such factors as the file size,resolution, or dimensions of the original image, or the currentlyavailable processing bandwidth of the system.

The image may also be preliminarily processed to verify the likelyexistence and position a leaf in the image, as well as the leaf'ssuitability for use in subsequent steps. In some embodiments, the imageis analyzed to locate a region matching the expected characteristics ofan image of a leaf, such as a generally green color and a relativelyuniform composition.

To further streamline processing, the image may be cropped to the regioncorresponding to a portion of the leaf on which subsequent steps arelikely to yield accurate results. For example, computer vision or otherimage processing techniques may be performed so as to exclude regions ofthe image that include stems, veins, damaged regions of the leaf, orother characteristics that may negatively affect processing. The imagemay also be resized to standardized dimensions to reduce the complexityof later processing steps.

At step 140, a chlorophyll concentration value of the leaf is estimatedbased on the first image of transmitted light through the leaf. In someembodiments, the RGB values R_(t), G_(t), B_(t) of the pixels of thefirst image are de-mosaicked to construct a full color image. (Thesubscript “t” denotes that these RGB values are derived from the firstimage, comprising light transmitted through the leaf). A chlorophyllconcentration of the leaf can be estimated from the R_(t), G_(t), B_(t)values.

A triangular green index (TGI) may be estimated from the R_(t), G_(t),B_(t) values. “A visible band index for remote sensing leaf chlorophyllcontent at the canopy scale” (2013), by Hunt, E. Raymond Jr., et al.,the disclosure of which is hereby incorporated by reference in theentirety. TGI is a spectral index for describing imaging spectrometrydata in the visible-band spectrum. In some embodiments, the relationshipof TGI to the RGB values of the transmissive image can be expressed as:

TGI_(t)=½(190(R _(t) −G _(t))−120(R _(t) −B _(t)))

A transmissive measure of chlorophyll a+b (Ctab) in the leaf from themay be estimated based on the value of TGI and one or more transmissivemodel coefficients related to a leaf model parameter N. N relates to anindex of refraction of the leaf, and may be a known or approximate valuethat varies by plant type, leaf structure, vascularization, and thelike. For example, a monocot plant may have an N of 1.5, whereas a dicotmay have an N of 3. In some embodiments, the relationship between Ctaband the coefficients may be expressed as a second order polynomialhaving three coefficients a, b, and c. In such embodiments, an initialvalue of N may be estimated based on known characteristics of the plantand/or leaf, and the corresponding transmissive model coefficients a, b,and c may be derived or accessed for that value of N. In someembodiments, a database of approximate N values and correspondingcoefficient values is accessed; coefficients for the N selected for usein the current model may be interpolated or otherwise estimated fromtransmissive model coefficients for known values of N. In otherembodiments, the coefficient values may be calculated using N and theR_(t), G_(r), B_(t) values.

An exemplary table of transmissive model coefficients for representativevalues of N is shown in Table 1:

TABLE 1 Exemplary transmissive coefficients for various values of N N aB c 1 0.006546 1.7687 138.71 1.5 0.011760 2.2295 127.28 2 0.0192202.7156 118.50 2.5 0.029778 3.2515 111.75 3 0.044475 3.8492 106.45

The value of TGI_(t) and the coefficients for a given N may be used incalculating the estimated chlorophyll, Ctab, in the leaf, where:

Ctab=a(TGI_(t) ²)+b(TGI_(t))+c

In some embodiments, one or more optical references are used to adjustthe value of Ctab by correlating the R_(t), G_(t), B_(t) values in thefirst image with R, G, B values obtained through media havingcharacteristics associated with known chlorophyll levels. For example,images may be captured through two semi-transparent films on an opticalreference card. An exemplary optical reference card 200 is seen in FIG.3. A first window 310 is provided that allows the transmission of lightin a manner that emulates the transmission of light a leaf having aknown low chlorophyll level of a plant, and a second window 320 isprovided that allows the transmission of light in a manner that emulatesthe transmission of light a leaf having a known high chlorophyll levelof a plant. In some embodiments, only a single window is provided. Thefirst window 310 and the second window 320 may be constructed ofplastic, vellum, paper, or other transparent or semi-transparentmaterial, and may be tinted or otherwise made to emulate thelight-transmissive characteristics of a leaf.

In embodiments where the optical reference card 300 is used, acorrection factor B to be used in calculating Ctab may be determined bythe RGB values of the images captured through the first window 310 andthe second window 320. For example, a linear error equation may beinterpolated between the RGB values of the images captured through thefirst window 310 and the second window 320 using the value of Ctabdetermined above. The interpolation yields the correction factor B for aknown value of N, which can be used to calculate a refined value ofCtab:

Ctab=a(TGI_(t) ²)+b(TGI_(t))+c+B

The correction factor B may allow for the correction of errors orinaccuracies in calculating the Ctab due to lighting conditions incapturing the first image.

Returning again to FIG. 1, at step 150 a reflectance chlorophyllconcentration value is estimated for the leaf based on the second imageof light reflected off the leaf. In some embodiments, the RGB valuesR_(r), G_(r), B_(r) of the pixels of the second image are de-mosaickedto construct a full color image. (The subscript “r” denotes that theseRGB values are derived from the second image, comprising light reflectedfrom the leaf). A chlorophyll concentration of the leaf can be estimatedusing the R_(r), G_(r), B_(r) values.

Measuring reflected light introduces the complication of bidirectionalreflectance, which includes such factors as the illumination zenithangle θ_(s), the incident angle θ_(i), and the bidirectional reflectancedistribution function (BRDF) parameter, Bspec. A Bspec value may bedetermined for each pixel in an image, and may vary greatly due tocertain reflectance phenomena. For example, Bspec for pixels in an imageof a leaf may have a maximum value of 0.6 in the center of a glint, andmay have a minimum value of 0 where the image is captured at highincidence angles, or where regions of the leaf are damaged. In otherembodiments, a different minimum value (e.g., 0.2) may be set for Bpsecfor pixels.

A reflectance measure of chlorophyll a+b (Crab) in the leaf from the maybe estimated based in part on the value of Bspec. Yet embodiments of thepresent disclosure avoid the inaccuracies associated with the widevariance in Bspec values described above by simultaneously estimatingBspec and Crab under the constraint of minimizing Crab variance acrossthe leaf surface. The level of chlorophyll across a relatively uniform,undamaged leaf may be presumed to be consistent. Determining Crab usingiterating estimated values of Bspec for each pixel of the second image,with the goal of minimizing variance in the Crab, therefore allows themethod to converge on an accurate estimate of Crab.

A method 400 of converging on an accurate estimate of Crab according toone embodiment is discussed with reference to FIG. 4.

At step 410, the method begins.

At step 420, the pixels of the first image are assigned an initialbidirectional reflectance parameter (Bspec) value. As discussed above,Bspec is related to the amount of light striking the sensor in theregion of the second image corresponding to the pixel. To continue theexample above, an area of glint or glare on the leaf in the image may beassigned a relatively high initial Bspec value (e.g., 0.6), whereas aregion that does not reflect as much light (due to incidence angle, leafdamage, or other factors) may be assigned a relatively lower initialBpsec value (e.g., 0.2). It will be appreciated that these numbers areused for exemplary purposes only, and a different range may be useddepending on lighting conditions, leaf type, leaf condition, or thelike.

At step 430, the initial Bspec value is used to estimate a first Crabvalue for some or all of the pixels in the second image. In someembodiments, a triangular green index value for the reflectance image(TGI_(r)) is estimated and is also used to estimate Crab. TGI_(r) may becalculated in much the same way that TGI_(r) is estimated in step 140above, by the relationship:

TGI_(r)=½(190(R _(r) −G _(r))−120(R _(r) −B _(r)))

In some embodiments, reflective model coefficients a, b, c are alsodetermined in order to express the relationship of TGI_(r) and Bspec toCrab for given values of N and Bspec. In some embodiments, a database ofN values and corresponding coefficient values is accessed; coefficientsfor the value of N selected for use in the current model may beinterpolated or otherwise estimated from reflective model coefficientsfor known values of N. In other embodiments, the coefficient values maybe calculated using N and the R_(r), G_(r), B_(r) values.

In one example, a particular strain of corn is known to have anapproximate N value of 1.518. Reflective coefficients a, b, c forvarious values of Bspec for N=1.518 may be accessed. An exemplary tableshowing exemplary coefficients is shown in Table 2:

TABLE 2 Exemplary reflective coefficients for various values of Bspecwhere N = 1.518 Bspec a b c 0.01 0.64482 −16.978 134.58 0.06 0.64482−19.684 173.05 0.11 0.64482 −22.39 217.19 0.16 0.64482 −25.097 267.020.21 0.64482 −27.803 322.52 0.26 0.64482 −30.509 383.69 0.31 0.64482−33.215 450.55 0.36 0.64482 −35.921 523.09 0.41 0.64482 −38.627 601.300.46 0.64482 −41.333 685.19 0.51 0.64482 −44.039 774.77

An estimate of Crab for each pixel may then be determined by arelationship between TGI_(r) and BSpec for that pixel, and thereflective coefficients:

Crab=a(TGI_(r) ²)+b(BSpec)+c(Bspec)

The reflective coefficients for the specific value of N in Table 2 areprovided for illustrative purposes only. Reflective coefficients can becalculated for any value of Bspec using the following meta-model for theterms above:

-   -   a=0.64482    -   b(Bspec)=−54.12(Bspec)−16.437    -   c(Bspec)=1135.7(Bspec²)+689(Bspec)+127

At step 440, a variance of the Crab estimate across the pixels isdetermined. For example, the variance may be calculated as the squareddeviation of Crab of each pixel from the mean Crab estimate for thepixels. Based on the consistent chlorophyll assumption, a determinationthat Crab estimates for individual pixels varies by a relatively largeamount from the mean may indicate that further refinement may benecessary. In some embodiments, the variance of the Crab estimates aswell as the mean Crab value may be stored for comparison in later steps.

At step 450, the initial Bspec value for each pixel may be modifiedaccording to the Crab estimate determined at step 430. For example, theBspec value may be reduced for pixels having a relatively high Crabvalue as determined at step 430. Similarly, the Bspec value may beincreased for pixels having a relatively low Crab value as determined atstep 430.

At step 460, the process repeats steps 430 and 440 using the modifiedBspec values from step 450. In particular, a revised Crab estimate isdetermined for each pixel using the modified Bspec values, and thevariance of these revised Crab estimates is determined. The variance ofthe revised Crab estimates is compared to the variance of any earlierCrab estimates, with the Crab estimates having a lower variance beingpreferred.

Steps 430, 440, and 450 may be repeated a number of times, with theBspec values of the pixels iteratively revised until an acceptably lowvariance of Crab estimates across the pixels is achieved. In thismanner, the method converges on a single Crab estimate. An average,median, mode, or other statistical measure of the low-variance Crabestimates can be performed to determine an estimated Crab value for theleaf. In some embodiments, once variance is minimized in this manner,the estimated Crab value for the leaf is determined only from thosepixels having a Bspec estimate within a given sigma variation from themean. In other words, outlier pixels that have a relatively extremevalue of Bspec (e.g., +/−a 1-sigma variation) are excluded fromcalculating the mean Crab estimate.

Method 400 ends at step 470.

It will be appreciated that the assumption of relatively constantchlorophyll levels across the leaf may be violated by leaf damage orother factors. Therefore, in some embodiments a pre-processing step maybe performed at the beginning of method 400 to identify low-variancepixels to be used in converging on a Crab estimate for the leaf. Forexample, pixels may be clustered (e.g., by a K-means algorithm)according to pixel properties, and only those pixels having propertiesvarying relatively little from the mean of that property for allcandidate pixels may be included in later steps.

Returning again to FIG. 1, at step 160, an estimated chlorophyllconcentration value for the plant is determined based on the Ctab valueestimated at step 140 and the Crab value estimated at step 150. Becausethe Ctab and Crab estimates are both attempts to measure the chlorophylla+b level of the leaf, the values should be similar. In someembodiments, the average of the Ctab estimate and the Crab estimate isdetermined to be the chlorophyll level of the plant. In otherembodiments, one of the two values (e.g., Ctab) may be determined to bethe chlorophyll level of the plant, with the other value (e.g. Crab)being a check or correction to the other value.

There may be some variation between the Ctab value estimated at step 140and the Crab value estimated at step 150. Such variation may indicate aninaccurate value of N, leading to selection of improper coefficients inestimating Crab and Ctab. In some embodiments, the value of N can beestimated based on the values of Crab and Crab so that:

N=0.0001(Ctab−Crab)²+0.0124(Ctab−Crab)+1.4878

At optional step 170, a refined value of the leaf model parameter N isestimated using this relationship, allowing for recalculation of thevalues of Ctab and Crab in steps 140 and 150 using coefficients based onthe refined value of N. This refinement process may be repeated untilthe values of Ctab and Crab for a given value of N are nearly identical.The value of N used in the initial run of the process may be a knownvalue of N for a given species of plant, but in reality the index ofrefraction (and therefore N) for a particular plant may vary from thepublished value of N.

Method 100 ends at step 180.

Method 100 provides a “spot measurement” of chlorophyll for one or moreleafs in a single location (e.g., from a single plant). According toanother aspect of the present disclosure, multiple spot measurements canbe taken at various locations around a field or region thereof, and themultiple spot measurements may be used to generate a chlorophyll profile(e.g., a map) of the entire field. GPS measurements or other locationdata may be used to correlate the spot measurements with locationscaptured in overhead imagery of the field, such as satellite or aerialimagery. Sensor spectral response measurements may be determined fromthe overhead imagery of the field. Ground-based measurements of the“Leaf Area Index” (the relative area covered by foliage in the field)may be used to refine the spectral response measurements of the overheadimagery.

The spot measurements can be used to correct or calibrate the overheadimagery to generate a full predictive model of the chlorophyll level ofthe field, which in turn can be used to determine the amount of nitrogenavailable to the plants at various locations in the field, as well asareas of nitrogen deficiency or surplus. Spot yield measurements and/orhistorical measurements of yield, chlorophyll level, nitrogen level, orother metrics may be used to further calibrate the full predictivemodel.

FIG. 5 illustrates an exemplary overhead model 500 of chlorophyll in afield according to some embodiments. The overhead model may have beendetermined using color and/or spectral response measurements of overheadimagery to determine its “greenness,” and from that, chlorophyllestimates for portions of the field. The model 500 includes regions502-512 for which different chlorophyll estimates have been made. Theshape, size, and characteristics of regions 502-512 are for illustrativepurposes only, and the model 500 may include chlorophyll measurementsfor regions encompassed by single pixels or pixel blocks of any suitablesize.

Locations 550 a-c in the field at which spot measurements may be takenare overlaid onto FIG. 5. The spot measurements may be individualchlorophyll estimates performed from images captured at each location asdetermined in method 100.

A method 600 of using spot chlorophyll measurements to generate achlorophyll map of a field according to one embodiment is discussed withreference to FIG. 6.

At step 610, the method begins.

At optional step 620, one or more locations and/or the number of thoselocations are selected for performing spot chlorophyll measurements inthe field. According to some embodiments, a Monte Carlo technique isperformed to estimate the effect on the chlorophyll model of the numberof spot measurements, spatial distribution and/or location of the spotmeasurements, and accuracy of the spot measurements. The Monte Carlosimulation is run based on various combinations of those variables, andthe predicted full chlorophyll model is compared to actual informationderived from spot measurements or otherwise. The output of the MonteCarlo simulation, and its correlation to actual information for aparticular combination of variables, allows for recommendations to bemade concerning the number of spot measurements needed, the best spotmeasurement location configurations, and the required accuracy ortolerance of the spot measurements. According to some embodiments, a mapof proposed spot measurements and/or GPS coordinates for taking thosemeasurements is provided. In some embodiments, instructions are providedto guide a person (e.g., using a display or audio component of a mobiledevice) taking the spot measurements to the proper locations for takingsuch measurements. In other embodiments, specific locations are notgiven, but certain constraints are described. For example, it may berecommended that 10 spot measurements be taken, with no spot measurementwithin 100 meters of another spot measurement.

At step 630, a spot measurement estimate of a chlorophyll concentrationvalue of the first plant in a first region in the field may bedetermined. The spot measurement may be taken at a location recommendedin step 620. As described in step 620, in some embodiments a number ofspot measurements may be taken. The spot measurement estimate of achlorophyll concentration value may be determined from images of lighttransmitted through and reflected from a leaf according to the steps ofmethod 100. A location, time, weather condition, lighting condition, orother aspect of the spot measurement may be determined (e.g., by using aGPS component) and stored with the spot measurement information.

At step 640, an overhead sensor spectral response of at least one secondplant in the first region in the field is detected from an overheadimage of the field. According to some embodiments, an overhead TGI valueis determined for the portions of the field according to the R, G, Bvalues of pixels in the overhead image. It will be appreciated, however,that an overhead image of the field is likely to contain regions ofvegetation (i.e., the crop plant whose chlorophyll is being measured) aswell as the bare earth in which the vegetation is growing. Since youngerplants are generally smaller than more mature plants, a field withrecently-planted crops is likely to contain more pixels representingearth (i.e., dirt) than a field with plants nearly ready for harvest.The different pixel characteristics associated with vegetation and earthlead to a “mixing problem” wherein the reflectance of non-crop materialmixes with the chlorophyll signature. The effect of the mixing problemcan be minimized by determining the TGI of only the portion of the fieldcovered by vegetation using the Leaf Area Index (LAI).

According to some embodiments, the TGI of the plants in the field isdetermined using ground based-measurements to correct TGI measurementsfrom overhead imagery. In particular, a ground-based image of at leastone plant and surrounding soil is captured, and a ground-based sensorspectral response measurement is determined. A mobile phone user may beinstructed to use a mobile device or other digital camera to capture animage from a relatively low angle of one or more rows of crops and thesurrounding earth. The image may be captured according to a typical userexperience of capturing an image, such as from a height of 3-5 feetabove the ground, aiming downward at the ground at a 45 degree anglebelow horizontal. The user may be instructed to stand between twoadjacent rows of crops. A gyroscope or 3-axis accelerometer within themobile device may be used to determine if the angle of the device isacceptable for capturing the image, or may be used to generateinstructions to the user to change the orientation of the mobile device.

According to some embodiments, a portion of a row of crops may beidentified in the image using sensor spectral response, color detection,computer vision techniques, or other techniques. According to someembodiments, the pixels of the ground-based image having a sensorspectral response corresponding to what a human would perceive as greenvegetation are detected, and the area they occupy in the image may bedetermined with respect to the remaining pixels.

At step 650, the ground-based image may be used to correct or adjust theTGI values of an overhead image. If the overhead image is of sufficientquality and resolution such that it is possible to identify rows ofcrops within the overhead image, then the position(s) and area (inpixels) of rows in the ground-based image may also be determined. Areasof vegetation can be detected (e.g., based on the sensor spectralresponse of the camera), and the portion of the row covered byvegetation can be expressed as LAI_(r). A TGI value for the plants maybe determined using LAI_(r), wherein the TGI of pixels corresponding tovegetation in individual rows of crops is determined according to thefollowing relationship:

${TGI}_{a} = \frac{\left( {{TGI}_{row} - {\left( {1 - {LAI}_{r}} \right){TGI}_{earth}}} \right)}{{LAI}_{r}}$

TGI_(row) represents the measured TGI on the portion of the imagecorresponding to the row, and TGI_(earth) represents the measured TGI ofthe visible earth between the rows as determined from the overheadimagery. TGI_(earth) can be obtained by transforming the ground-basedimage R, G, B measurements of earth to an estimated response of theoverhead sensor pixel when viewing just earth.

In other cases, the overhead image may be of insufficient quality ofresolution to resolve individual rows. In that case, a field-based TGImay be determined using LAI_(f), wherein the TGI of pixels correspondingto vegetation in the field is determined according to the followingrelationship:

${TGI}_{a} = \frac{\left( {{TGI}_{row} - {\left( {1 - {LAI}_{r}} \right){TGI}_{earth}}} \right)}{{LAI}_{r}}$

TGI_(field) represents the measured TGI of the field generally, andTGI_(earth) represents the measured TGI of the visible earth (i.e.,non-vegetation) as determined from the overhead imagery.

Under either model, TGI_(a) isolates the TGI of the vegetation byreducing the mixing effect of using pixels representing vegetation andearth to calculate TGI. In some embodiments, both a row-based andfield-based TGI is determined, with a confidence level determined forthe row-based TGI depending on the resolution of the image and otherfactors. The confidence level is used to determine if the row-based TGIor field-based TGI is to be used for subsequent steps.

At step 660, a full chlorophyll model is determined based on theadjusted overhead TGI values and the spot measurements of chlorophyllvalues. In particular, a 2D interpolation is performed using theoverhead TGI values as dependent variables and using the spotmeasurement chlorophyll values determined in step 630 (according tomethod 100) as independent variables. For example, an nth orderregression model may be employed. In some embodiments, overhead measuresof plant health (such as NDVI or TGI) are positively correlated toground-based measures of yield, or greenness. Regression models withoutthis constraint may have a good fit to the data, but may givecounter-intuitive results for areas in the field having low indicatedplant health but high predicted yield or chlorophyll. In someembodiments, such results are avoided by constraining the Nth ordermodel to have N+1 positive correlation coefficients, P(1) . . . P(N+1)such that:

Y=P(1)*X ^(N) +P(2)*X ^((N-1)) + . . . +P(N)*X+P(N+1)

where Y is a vector of M spot measurements (M>N) at M field locations,and X is a vector of overhead measurements (space or aerial) of NDVI,TGI or other plant health indicator at the same M field locations. Thespot measurements can be yield estimates from the kernel counter, orchlorophyll estimates.

The N+1 coefficient values are solved using a non-negative least squaresalgorithm. The algorithm starts with a set of possible basis vectors andcomputes the associated dual vector lambda. The algorithm then selectsthe basis vector corresponding to the maximum value in lambda in orderto swap out of the basis in exchange for another possible candidate.This continues until lambda is less than or equal to zero. Furthermore,the spot measurements are tested to ensure they cover the full range ofexpected values. Spot yield measurements may range from a minimum valueYmin to a maximum value Ymax. If the spot measurement vector does notspan this range, then Ymin and Ymax are artificially appended. For cornyield, Ymin and Ymax are 50, and 250 bushels/acre, respectively. Forchlorophyll, Ymin, and Ymax are 20 and 80 micrograms/cm², respectively.The X vector may also be expanded when the Y vector is expanded.

For yield, when the overhead plant health measurements are NDVI, Xminand Xmax are 0.3 and 0.9, respectively. For chlorophyll, when theoverhead plant health measurements are TGI, the Xmin and Xmax depends onthe average Bspec parameter but is generally between 5 and 25respectively for average overhead Bspec values less than 0.3. In thismanner, overhead TGI values can be used to estimate chlorophyll valuesin the full chlorophyll model, with the spot measurement chlorophyllvalues being used to calibrate the model.

The method ends at step 670.

The full chlorophyll model determined in method 600 may be used togenerate a nitrogen sufficiency map for the crop, which indicates anestimated amount of nitrogen available to plants in certain regions ofthe field. In some embodiments, it is recommended to grow a control plotof the crop that has sufficient nitrogen, such as by over-applyingnitrogen. The control plot may be designed to represent the cropgenerally according to one or more aspects, including soil acidity,inherent soil nitrogen content, sunlight, moisture content, and othersoil conditions. The control plot may also be part of the larger fieldfor which a full chlorophyll model is generated in method 600. Theestimated chlorophyll content of the control plot can then be dividedinto the chlorophyll estimates of other portions of the field togenerate a nitrogen sufficiency profile (e.g., map) providing a nitrogensufficiency value N_(s) for other portions of the field. The value N_(s)may range from 0.0 to 1.0, wherein the nitrogen content of the controlplot is defined as 1.0. Regions of the nitrogen sufficiency profilehaving a value of N_(s) less than a defined threshold (e.g., 0.9) may beconsidered for side-dress. In general, the nitrogen application rate maybe determined according to the following relationship:

N _(r)=200(1−N _(s))

where N_(r), may be expressed in terms of pounds of nitrogen per acre.

In embodiments where no control plot is available, the interpretation ofthe chlorophyll results may be determined based at least on the type ofcrop. For example, it may be determined that for corn, at least 50micrograms/cm² of Chlorophyll a+b (Cab) is needed for healthy growth.This target may be used as a normalization factor to product a nitrogensufficiency map and nitrogen recommendation profile.

In some embodiments, spot measurements of yield estimates of the cropmay be used to further calibrate the full chlorophyll model. Yieldestimates of grain crop plants (e.g., wheat, corn, rice, or any othergrain crop having a seed head) or other plants having seed pods (e.g., acotton boll) may be determined using methods for automaticallyestimating a number of seed heads (e.g., corn kernels) using a digitalcamera of a mobile device. Apparatus and processes for performing suchmethods are described in U.S. application Ser. No. 15/011,004, filed onJan. 29, 2016 and titled “APPARATUS AND PROCESSES FOR CLASSIFYING ANDCOUNTING CORN KERNELS”, the contents of which are hereby incorporated intheir entirety for all purposes.

The spot yield measurements can be 2D interpolated to give a field mapof predicted yield. In particular, a regression may be performed withthe overhead TGI values as dependent variables and using spot yieldmeasurements as independent variables. For example, a first- orsecond-order regression model may be employed. It will be appreciatedthat any measure of plant health index other than TGI may also be used.For example, the Normalized Vegetation Difference Index (NDVI) may beused as an index of plant health, and may be expressed as:

${NDVI} = \frac{{NIR} - R}{{NIR} + R}$

where R and NIR represent the spectral reflectance measurements acquiredin the red and near-infrared regions, respectively.

In some embodiments, historical data for the field and/or crop may alsobe determined. For example, profiles or maps of previous measurements ofyield, chlorophyll, nitrogen sufficiency, or nitrogen application may beemployed to modify any nitrogen recommendations determined from thechlorophyll model. In some embodiments, the full yield model and/or thehistorical data may be used to calibrate the nitrogen application rate.For example, if the chlorophyll model leads suggests that a particularamount of nitrogen be applied, but historical data from a previous yearindicates that the yield that year was sufficient using a lower amountof nitrogen, the nitrogen amount suggested may be reduced for thecurrent year. Similarly, if the full yield model for the current yearsuggests that the yield is estimated to be less than sufficient, thenitrogen amount suggested may be increased for the current year.

According to some embodiments, the historical data may be assigned arelevance score or other measure of its applicability to the currentyear. For example, historical data from a year with a large amount ofprecipitation may be given a relatively low relevance score if thecurrent year is experience drought conditions. Similarly, the presenceof unforeseen factors in the historical data, such as hail, pest damage,wind, flooding, or the like may also reduce the relevance score of thatyear where the present year does not include such factors.

FIG. 7 is a block diagram of a distributed computer system 700, in whichvarious aspects and functions discussed above may be practiced. Thedistributed computer system 700 may include one or more computersystems. For example, as illustrated, the distributed computer system700 includes three computer systems 702, 704 and 706. As shown, thecomputer systems 702, 704 and 706 are interconnected by, and mayexchange data through, a communication network 708. The network 708 mayinclude any communication network through which computer systems mayexchange data. To exchange data via the network 708, the computersystems 702, 704, and 706 and the network 708 may use various methods,protocols and standards including, among others, token ring, Ethernet,Wireless Ethernet, Bluetooth, radio signaling, infra-red signaling,TCP/IP, UDP, HTTP, FTP, SNMP, SMS, MMS, SS7, JSON, XML, REST, SOAP,CORBA IIOP, RMI, DCOM and Web Services.

According to some embodiments, the functions and operations discussedfor producing a three-dimensional synthetic viewpoint can be executed oncomputer systems 702, 704 and 706 individually and/or in combination.For example, the computer systems 702, 704, and 706 support, forexample, participation in a collaborative network. In one alternative, asingle computer system (e.g., 702) can generate the three-dimensionalsynthetic viewpoint. The computer systems 702, 704 and 706 may includepersonal computing devices such as cellular telephones, smart phones,tablets, “fablets,” etc., and may also include desktop computers, laptopcomputers, etc.

Various aspects and functions in accord with embodiments discussedherein may be implemented as specialized hardware or software executingin one or more computer systems including the computer system 702 shownin FIG. 7. In one embodiment, computer system 702 is a personalcomputing device specially configured to execute the processes and/oroperations discussed above. As depicted, the computer system 702includes at least one processor 710 (e.g., a single core or a multi-coreprocessor), a memory 712, a bus 714, input/output interfaces (e.g., 716)and storage 718. The processor 710, which may include one or moremicroprocessors or other types of controllers, can perform a series ofinstructions that manipulate data. As shown, the processor 710 isconnected to other system components, including a memory 712, by aninterconnection element (e.g., the bus 714).

The memory 712 and/or storage 718 may be used for storing programs anddata during operation of the computer system 702. For example, thememory 712 may be a relatively high performance, volatile, random accessmemory such as a dynamic random access memory (DRAM) or static memory(SRAM). In addition, the memory 712 may include any device for storingdata, such as a disk drive or other non-volatile storage device, such asflash memory, solid state, or phase-change memory (PCM). In furtherembodiments, the functions and operations discussed with respect togenerating and/or rendering synthetic three-dimensional views can beembodied in an application that is executed on the computer system 702from the memory 712 and/or the storage 718. For example, the applicationcan be made available through an “app store” for download and/orpurchase. Once installed or made available for execution, computersystem 702 can be specially configured to execute the functionsassociated with producing synthetic three-dimensional views.

Computer system 702 also includes one or more interfaces 716 such asinput devices (e.g., camera for capturing images), output devices andcombination input/output devices. The interfaces 716 may receive input,provide output, or both. The storage 718 may include a computer-readableand computer-writeable nonvolatile storage medium in which instructionsare stored that define a program to be executed by the processor. Thestorage system 718 also may include information that is recorded, on orin, the medium, and this information may be processed by theapplication. A medium that can be used with various embodiments mayinclude, for example, optical disk, magnetic disk or flash memory, SSD,among others. Further, aspects and embodiments are not to a particularmemory system or storage system.

In some embodiments, the computer system 702 may include an operatingsystem that manages at least a portion of the hardware components (e.g.,input/output devices, touch screens, cameras, etc.) included in computersystem 702. One or more processors or controllers, such as processor710, may execute an operating system which may be, among others, aWindows-based operating system (e.g., Windows NT, ME, XP, Vista, 7, 8,or RT) available from the Microsoft Corporation, an operating systemavailable from Apple Computer (e.g., MAC OS, including System X), one ofmany Linux-based operating system distributions (for example, theEnterprise Linux operating system available from Red Hat Inc.), aSolaris operating system available from Sun Microsystems, or a UNIXoperating systems available from various sources. Many other operatingsystems may be used, including operating systems designed for personalcomputing devices (e.g., iOS, Android, etc.) and embodiments are notlimited to any particular operating system.

The processor and operating system together define a computing platformon which applications (e.g., “apps” available from an “app store”) maybe executed. Additionally, various functions for generating andmanipulating images may be implemented in a non-programmed environment(for example, documents created in HTML, XML or other format that, whenviewed in a window of a browser program, render aspects of agraphical-user interface or perform other functions). Further, variousembodiments in accord with aspects of the present invention may beimplemented as programmed or non-programmed components, or anycombination thereof. Various embodiments may be implemented in part asMATLAB functions, scripts, and/or batch jobs. Thus, the invention is notlimited to a specific programming language and any suitable programminglanguage could also be used.

Although the computer system 702 is shown by way of example as one typeof computer system upon which various functions for producingthree-dimensional synthetic views may be practiced, aspects andembodiments are not limited to being implemented on the computer system,shown in FIG. 7. Various aspects and functions may be practiced on oneor more computers or similar devices having different architectures orcomponents than that shown in FIG. 7.

Having described above several aspects of at least one embodiment, it isto be appreciated various alterations, modifications, and improvementswill readily occur to those skilled in the art. Such alterations,modifications, and improvements are intended to be part of thisdisclosure and are intended to be within the scope of the invention.Accordingly, the foregoing description and drawings are by way ofexample only, and the scope of the invention should be determined fromproper construction of the appended claims, and their equivalents.

What is claimed is:
 1. A method for determining chlorophyll content of aplant, comprising: capturing a first image comprising light transmittedthrough a leaf of a plant; capturing a second image comprising lightreflected from the leaf of the plant; estimating, from a plurality ofpixels in the first image, a transmissive chlorophyll concentrationvalue of the leaf; estimating a reflectance chlorophyll concentrationvalue for the leaf from a plurality of pixels in the second image usingbidirectional reflectance parameters for which a variance of thereflectance chlorophyll concentration value across the plurality ofpixels in the second image is reduced; and determining an estimatedchlorophyll concentration value for the plant based at least on thetransmissive chlorophyll concentration value and the reflectancechlorophyll concentration value.
 2. The method of claim 1, wherein thetransmissive chlorophyll concentration value and the reflectancechlorophyll concentration value are determined using a leaf modelparameter, further comprising: estimating, from the transmissivechlorophyll concentration value and the reflectance chlorophyllconcentration value, a revised leaf model parameter; and determining asecond transmissive chlorophyll concentration value and a secondreflectance chlorophyll concentration value using the revised leaf modelparameter.
 3. The method of claim 2, wherein the revised leaf modelparameter is estimated based on a difference between the transmissivechlorophyll concentration value and the reflectance chlorophyllconcentration value.
 4. The method of claim 1, wherein estimating, fromthe plurality of pixels in the first image, the transmissive chlorophyllconcentration value of the leaf comprises determining, from sensorspectral response characteristics of each pixel in the plurality ofpixels in the first image, a triangular greenness index (TGI) for thepixel.
 5. The method of claim 1, further comprising: capturing a thirdimage comprising light passed through a first medium and a fourth imagecomprising light passed through a second medium, the first medium andsecond medium having transmissive characteristics corresponding to knowntransmissive chlorophyll levels; and adjusting the transmissivechlorophyll concentration value of the leaf with reference to the knowntransmissive chlorophyll levels.
 6. The method of claim 5, wherein thefirst medium has transmissive characteristics corresponding to a knownlow transmissive chlorophyll level, and wherein the second medium hastransmissive characteristics corresponding to a known high transmissivechlorophyll level.
 7. The method of claim 1, further comprising:estimating, using a bidirectional reflectance parameter for each pixelin the plurality of pixels, a first reflectance chlorophyllconcentration pixel value for each pixel in the plurality of pixels;determining a first variance of the first reflectance chlorophyllconcentration pixel value across the plurality of pixels; modifying thebidirectional reflectance parameter for at least one pixel in theplurality of pixels; estimating, using the modified bidirectionalreflectance parameter for the at least one pixel, a second reflectancechlorophyll concentration pixel value for each pixel in the plurality ofpixels; determining a second variance of the second reflectancechlorophyll concentration pixel value across the plurality of pixels;responsive to the first variance being less than the second variance,estimating the reflectance chlorophyll concentration value based on thefirst reflectance chlorophyll concentration pixel value of the leaf foreach pixel in the plurality of pixels; and responsive to the secondvariance being less than the first variance, estimating the reflectancechlorophyll concentration value based on the second reflectancechlorophyll concentration pixel value of the leaf for each pixel in theplurality of pixels.
 8. The method of claim 7, wherein modifying thebidirectional reflectance parameter for at least one pixel in theplurality of pixels comprises: responsive to the at least one pixel inthe plurality of pixels having a relatively high first reflectancechlorophyll concentration pixel value, adjusting the bidirectionalreflectance parameter of the at least one pixel to be lower; andresponsive to the at least one pixel in the plurality of pixels having arelatively low first reflectance chlorophyll concentration pixel value,adjusting the bidirectional reflectance parameter of the at least onepixel to be higher.
 9. The method of claim 7, wherein estimating thereflectance chlorophyll concentration value based on the secondreflectance chlorophyll concentration pixel value of the leaf for eachpixel in the plurality of pixels comprises determining a mean of thesecond reflectance chlorophyll concentration pixel value of the leaf forthe plurality of pixels.
 10. The method of claim 9, further comprisingexcluding, from the determination of the mean, pixels having a modifiedbidirectional reflectance parameter not within a defined deviationamount.
 11. The method of claim 7, wherein the bidirectional reflectanceparameter is an initial bidirectional reflectance parameter, furthercomprising setting an initial bidirectional reflectance parameter for atleast one pixel in the plurality of pixels, the initial bidirectionalreflectance parameter determined by the sensor spectral responsemeasurement of the at least one pixel.
 12. The method of claim 11,further comprising setting a first initial bidirectional reflectanceparameter of 0.6 for at least one pixel having a highest sensor spectralresponse measurement in the plurality of pixels, and setting a secondinitial bidirectional reflectance parameter of 0.0 for at least onepixel having a lowest sensor spectral response measurement in theplurality of pixels.
 13. The method of claim 1, wherein the plant is afirst plant further comprising: estimating a second transmissivechlorophyll concentration value and a second reflectance chlorophyllconcentration value for at least a second plant in a crop fieldincluding the first plant; and generating a model of plant health forthe crop field based at least on the transmissive chlorophyllconcentration value, the reflectance chlorophyll concentration value,the second transmissive chlorophyll concentration value and the secondreflectance chlorophyll concentration value.
 14. The method of claim 13,wherein the model of plant health for the crop field is a chlorophyllmodel indicating an estimated chlorophyll level of plants in a pluralityof locations in the crop field.
 15. The method of claim 1, wherein theplant is a corn plant.
 16. An image processing system comprising: amemory; an image receiving component; and a processor configured to:capture a first image comprising light transmitted through a leaf of aplant; capture a second image comprising light reflected from the leafof the plant; estimate, from a plurality of pixels in the first image, atransmissive chlorophyll concentration value of the leaf; estimate areflectance chlorophyll concentration value for the leaf from aplurality of pixels in the second image using bidirectional reflectanceparameters for which a variance of the reflectance chlorophyllconcentration value across the plurality of pixels in the second imageis reduced; and determine an estimated chlorophyll concentration valuefor the plant based at least on the transmissive chlorophyllconcentration value and the reflectance chlorophyll concentration value.17. The image processing system of claim 16, wherein the image receivingcomponent is a digital camera of a mobile device.
 18. The imageprocessing system of claim 16, further comprising an optical referencehaving a first medium and a second medium, the first medium and secondmedium having transmissive characteristics corresponding to knowntransmissive chlorophyll levels, wherein the processor is furtherconfigured to: capture a third image comprising light passed through thefirst medium and a fourth image comprising light passed through thesecond medium; and adjust the transmissive chlorophyll concentrationvalue of the leaf with reference to the known transmissive chlorophylllevels.
 19. The image processing system of claim 16, wherein theprocessor is further configured to: estimate, using a bidirectionalreflectance parameter for each pixel in the plurality of pixels, a firstreflectance chlorophyll concentration pixel value for each pixel in theplurality of pixels; determine a first variance of the first reflectancechlorophyll concentration pixel value across the plurality of pixels;modify the bidirectional reflectance parameter for at least one pixel inthe plurality of pixels; estimate, using the modified bidirectionalreflectance parameter for the at least one pixel, a second reflectancechlorophyll concentration pixel value for each pixel in the plurality ofpixels; determine a second variance of the second reflectancechlorophyll concentration pixel value across the plurality of pixels;responsive to the first variance being less than the second variance,estimate the reflectance chlorophyll concentration value based on thefirst reflectance chlorophyll concentration pixel value of the leaf foreach pixel in the plurality of pixels; and responsive to the secondvariance being less than the first variance, estimate the reflectancechlorophyll concentration value based on the second reflectancechlorophyll concentration pixel value of the leaf for each pixel in theplurality of pixels.
 20. The image processing system of claim 19,wherein the processor is further configured to modify the bidirectionalreflectance parameter for at least one pixel in the plurality of pixelsby: responsive to the at least one pixel in the plurality of pixelshaving a relatively high first reflectance chlorophyll concentrationpixel value, adjusting the bidirectional reflectance parameter of the atleast one pixel to be lower; and responsive to the at least one pixel inthe plurality of pixels having a relatively low first reflectancechlorophyll concentration pixel value, adjusting the bidirectionalreflectance parameter of the at least one pixel to be higher.
 21. Amethod of determining a nitrogen content of a field crop, comprising:determining, from an image of an individual plant leaf from a firstplant in a field, an estimate of a chlorophyll concentration value ofthe first plant in a first region in the field; detecting, in anoverhead image of the field, an overhead sensor spectral responsemeasurement of at least one second plant in the first region in thefield; and generating, based on the estimate of the chlorophyllconcentration value of the individual plant leaf and the overhead sensorspectral response measurement of the at least one second plant, a map ofestimated chlorophyll concentrations of plants in a portion of thefield.
 22. The method of claim 21, wherein the overhead sensor spectralresponse measurement of the at least one second plant is a triangulargreen index (TGI).
 23. The method of claim 21, further comprising:determining, from a ground-based image of at least one third plant andsurrounding soil in the first region, a ground-based sensor spectralresponse measurement of the at least one third plant; and adjusting theoverhead sensor spectral response measurement of the at least one secondplant based on the ground-based sensor spectral response measurement.24. The method of claim 23, further comprising identifying at least onedimension of a row of plants in which the at least one third plant islocated.
 25. The method of claim 21, further comprising generating,based on the map of estimated chlorophyll concentrations of plants in aportion of the field, at least one recommendation for applying nitrogento the first region of the field.
 26. The method of claim 25, furthercomprising: determining, from an image of a grain seed head of a thirdplant in the first region of the field, an estimated yield of the thirdplant; and modifying the at least one recommendation for applyingnitrogen to the first region of the field based on the estimated yieldof the third plant.